13,573 research outputs found
Analytical results for long time behavior in anomalous diffusion
We investigate through a Generalized Langevin formalism the phenomenon of
anomalous diffusion for asymptotic times, and we generalized the concept of the
diffusion exponent. A method is proposed to obtain the diffusion coefficient
analytically through the introduction of a time scaling factor . We
obtain as well an exact expression for for all kinds of diffusion.
Moreover, we show that is a universal parameter determined by the
diffusion exponent. The results are then compared with numerical calculations
and very good agreement is observed. The method is general and may be applied
to many types of stochastic problem
The influence of statistical properties of Fourier coefficients on random surfaces
Many examples of natural systems can be described by random Gaussian
surfaces. Much can be learned by analyzing the Fourier expansion of the
surfaces, from which it is possible to determine the corresponding Hurst
exponent and consequently establish the presence of scale invariance. We show
that this symmetry is not affected by the distribution of the modulus of the
Fourier coefficients. Furthermore, we investigate the role of the Fourier
phases of random surfaces. In particular, we show how the surface is affected
by a non-uniform distribution of phases
Localization properties of a tight-binding electronic model on the Apollonian network
An investigation on the properties of electronic states of a tight-binding
Hamiltonian on the Apollonian network is presented. This structure, which is
defined based on the Apollonian packing problem, has been explored both as a
complex network, and as a substrate, on the top of which physical models can
defined. The Schrodinger equation of the model, which includes only nearest
neighbor interactions, is written in a matrix formulation. In the uniform case,
the resulting Hamiltonian is proportional to the adjacency matrix of the
Apollonian network. The characterization of the electronic eigenstates is based
on the properties of the spectrum, which is characterized by a very large
degeneracy. The rotation symmetry of the network and large number of
equivalent sites are reflected in all eigenstates, which are classified
according to their parity. Extended and localized states are identified by
evaluating the participation rate. Results for other two non-uniform models on
the Apollonian network are also presented. In one case, interaction is
considered to be dependent of the node degree, while in the other one, random
on-site energies are considered.Comment: 7pages, 7 figure
Local roughness exponent in the nonlinear molecular-beam-epitaxy universality class in one-dimension
We report local roughness exponents, , for three
interface growth models in one dimension which are believed to belong the
non-linear molecular-beam-epitaxy (nMBE) universality class represented by the
Villain-Lais-Das Sarma (VLDS) stochastic equation. We applied an optimum
detrended fluctuation analysis (ODFA) [Luis et al., Phys. Rev. E 95, 042801
(2017)] and compared the outcomes with standard detrending methods. We observe
in all investigated models that ODFA outperforms the standard methods providing
exponents in the narrow interval consistent
with renormalization group predictions for the VLDS equation. In particular,
these exponent values are calculated for the Clarke-Vvdensky and Das
Sarma-Tamborenea models characterized by very strong corrections to the
scaling, for which large deviations of these values had been reported. Our
results strongly support the absence of anomalous scaling in the nMBE
universality class and the existence of corrections in the form
of the one-loop renormalization group analysis
of the VLDS equation
- …